The principal is $145 .
Simple interest is the interest amount for a particular principal amount of money at rate of interest. The interest is calculated by multiplying the principal with the time and rate. The total amount after a certain time is given by the sum of the principal and the interest for that time.
The formula for calculating the Interest on a Principal(P) , time(t) and rate(R).
Interest=P×R×t
Now let us consider the principal to be P.
Time(t)=5 years
Simple Interest(I)=$87
Rate(R)=12%=0.12
Now let us find the principle for the this interest using the above formula.
I=P×R×t
Substituting the given values we calculate the Principal(P).
[tex]87=P\times0.012\times5\\or,P=87\div(0.012\times5)\\or,P=87\div0.6\\or,P=145[/tex]
Therefore the Principal for the simple interest of $87 for 5 years at rate of 12% is $145.
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write an equation that is parallel to y=-5/2x-5
A parallel equation (when graphed) will have the same slope, but a different y-intercept.
As long as you keep y = -[tex]\frac{5}{2}[/tex]x + b, you can input anything for b to solve this question.
Given:
y = -[tex]\frac{5}{2}[/tex]x - 5
Equation of a parallel line:
y = -[tex]\frac{5}{2}[/tex]x + 6, y = -[tex]\frac{5}{2}[/tex]x + 1,356, y = -[tex]\frac{5}{2}[/tex]x - 8, etc
Example answer you can use:
y = -[tex]\frac{5}{2}[/tex]x - 8
Solve for F: C=5/9(F-32)
Answer:
F=9/5c+32
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
9/5C = F-32
C=F−32
Then add 32 to both sides, giving you:
9/5C + 32 = F
C+32=F
Thus, you have:
F= 9/5C + 32F=
5
9
C+32
Answer:
[tex]F= \frac{9}{5}C + 32[/tex]
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
[tex]\frac{9}{5}C = F-32[/tex]
Then add 32 to both sides, giving you:
[tex]\frac{9}{5}C + 32 = F[/tex]
Thus, you have:
[tex]F= \frac{9}{5}C + 32[/tex]
Use the following information to write an equation in terms of X. Then solve the equation and find RS and RT.
RS = 2x - 8
ST = 11
RT = x + 10
equation:?
x=?
RS=
RT=
We get the values of RS and RT as 6 and 17 respectively after solving the equations.
We are given the equations:
RS = 2x - 8
ST = 11
RT = x + 10
Now, we know that:
RS + ST = RT.
Substituting the values, we get that:
2 x - 8 + 11 = x + 10
2 x + 3 = x + 10
2 x - x = 10 - 3
x = 7
Now substituting it to find RS and RT:
RS = 2 x - 8
RS = 2 ( 7 ) - 8
RS = 14 - 8
RS = 6
RT = x + 10
RT = 7 + 10
RT = 17
Therefore, we get the values of RS and RT as 6 and 17 respectively after solving the equations.
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Question 13 (1 point)
Saved
Given the following definitions:
U= (a, b, c, d, e, f, g)
A = {a, c, e, g)
B = (a, b, c, d]
Find A U B'
Answer:
{a, c, e, f, g}
Step-by-step explanation:
[tex]B'=\{a,b,c,d,e,f,g\}-\{a,b,c,d\}=\{e,f,g\} \\ \\ A \cup B=\{a,c,e,f,g\}[/tex]
A rectangular solar panel has a length that is 12 inches shorter than 3 times its width. If the perimeter of the panel is 132 inches what are the dimensions of the panel?
Answer: 46.5 by 19.5
Step-by-step explanation:
P=perimeter of panel. L=length. W=width
L=3W-12
P=2L+2W
132=2(3W-12)+2W
132=6W-24+2W
132=6W+2W-24
132=8W-24
156=8W
W=19.5
P=2L+2W
132=2L+2(19.5)
132=2L+39
2L=93
L=46.5
46.5 by 19.5
5000 nails in five boxes. the first and second boxes have 2700 nails all together. the second and the third boxes have 2000 nails all together. the third and fourth boxes have 1800 nails all together. the fourth and the fifth boxes have 1700 nails all together. how many nails are in each box
The number of nails in each box is: 1300, 1400, 600, 1200, and 500
Given 5000 nails in five boxes.
Let X denote the universal set.
Then n(X) = 5000.
Let A denote the first box,
B denote the second box,
C denote the third box,
D denote the fourth box, and
E denotes the fifth box.
The first and second boxes have 2700 nails altogether.
⇒n(A ∪ B) = 2700
The second and third boxes have 2000 nails altogether.
⇒n(B ∪ C) = 2000
The third and fourth boxes have 1800 nails altogether.
⇒n(C ∪ D) = 1800
The fourth and fifth boxes have 1700 nails altogether.
⇒n(D ∪ E) = 1700
We need to find out how many nails are there in each box.
That is to find out: n(A), n(B), n(C), n(D), and n(E).
Note that all these five sets are disjoint. This means that the intersection is empty.
n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500
n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500
n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200
n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600
n(B) = n(B U C) - n(C) = 2000 - 600 = 1400
n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300
Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.
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A 5.ft tall man casts a shadow along the ground that is 8 ft. long. At the same time a giraffe casts a shadow that is 12 ft. long. How tall is the Giraffe?
Answer : 7.5 ft
Step-by-step explanation:
when the length of the shadow is 8ft, the actual height of the man = 5ft
8:5
let the giraffe be 'x' ft tall.
if the length of the shadow is 12ft, actual height = x ft
12:x
8:5 x 12:x
[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]
x= [tex]\frac{15}{2}[/tex]
x=7.5 ft
Therefore, the giraffe is 7.5ft tall.
Answer:
[tex]7.5\; {\rm ft}[/tex].
Step-by-step explanation:
The height of objects nearby under the sun are approximately proportional to the length of their shadows.
In other words, if the man and the giraffe are near each other and under the sun:
[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].
Given that:
[tex](\text{height of man}) = 5\;{\rm ft}[/tex], [tex](\text{length of shadow of man}) = 8\;{\rm ft}[/tex], and [tex](\text{length of shadow of giraffe}) = 12\; {\rm ft}[/tex].Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:
[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].
Fill in the blank set of stamps below with the value that would make the sets equal.
The number in each of the set of blank boxes is 10
How to find the number set equivalent?
From the first number set of stamps, we see that the sum of each row is;
5 + 5 + 5 + 5 = 20
There are four rows. Thus;
Total sum of set of stamps = 20 + 20 + 20 + 20
Total sum of set of stamps = 80
Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.
If the number in each box is x, then;
8x = 80
x = 80/8
x = 10
Thus, the number in each of the set of blank boxes is 10
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Simplifiy the expression 1/2 cubed - 6 divide √64
Answer:
[tex]-\frac{47}{64}[/tex] or [tex]\frac{1}{2}^{3} -6/\sqrt{64}[/tex]
Step-by-step explanation:
Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary to produce the graph.
please I need help
In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3
How to find the equation of the graphed function?
In the graph, we can see a parabola.
We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.
Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:
y = a*(x - h)^2 + k
In the image we can see that the vertex is (2, -3), then:
y = a*(x - 2)^2 - 3
And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then the quadratic equation is y = (x - 2)^2 - 3
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Which is the least whole number that rounds to 2000 when rounded to the nearest hundred
The required number is 2001.
To solve this problem we need to know the concept of rounding off.
Rounding off a number means making the value of number equal to the nearest tens place.
When we round off 45 we will get 50; when we round off 44 we get 40.
So, if a number has 5 at its unit place then it will be rounded off to the tens place which is ahead of 5 and if a number is less than 5 then it is rounded off to the tens place before that number.
Here it is asked to find the least whole number that rounds off to 2000 when rounded off to nearest hundred which will be 2001.
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Jaylan makes limeade using 3/4 cup of water for every 1/5 cup of lime juice. Rene's limeade recipe is different. He uses 2/3 cup of water for every 1/6 cup of lime juice.
whose limeade has a weaker flavor
Rene's limeade has a weaker flavor as calculated by division of fractions.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers. It's not necessary for this number to be an integer.When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient,Which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.Concentration of Jaylan's limeade [tex]=\frac{3}{4} \div\frac{1}{5} = \frac{15}{4} =3.75[/tex]
Therefore as calculated by division of fractions, concentration of Jaylan's limeade is 3.75 cups of water for 1 cup of lime juice.
Concentration of Rene's Limeade[tex]=\frac{2}{3} \div\frac{1}{6} = \frac{12}{3} =4[/tex]
Therefore as calculated by division of fractions, concentration of Rene's limeade is 4 cups of water for 1 cup of lime juice.
Hence Rene's limeade has a weaker flavor as calculated by division of fractions.
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How many times larger is 8 x 10^5 than 4 x 10^3?
The value 8 x 10^5 is 200 times greater than 4 x 10^3
Scientific notationsThe standard scientific notation is expressed as A * 10^n
where
A is the values between 1 and 10
n is any integer
In order to determine how many times larger is 8 x 10^5 than 4 x 10^3, we will take the ratio;
Ratio = 8 x 10^5/4 * 10^3
Ratio = 8/4 * 10^5/10^3
Ratio = 2 * 10^2
Ratio = 200
Hence the value 8 x 10^5 is 200 times greater than 4 x 10^3
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On average, Carmen can drive 33 miles on every gallon of gasoline. If she fills up her tank for $2.29 per gallon, how much will it cost her to drive 429 miles?
Answer:
$29.77
Step-by-step explanation:
First, divide 429 by 33 to find how many gallons that she's paying for, then multiply that by $2.29 to find the answer.
The cost for Carmen to drive 429 miles is $29.77.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Given that,
Distance car travels per gallon = 33 miles per gallon
Cost of gasoline per gallon = $2.29 per gallon.
33 miles can be travelled with 1 gallon of gasoline.
1 mile can be travelled with 1/33 gallon of gasoline.
429 miles can be travelled with 429/33 = 13 gallon of gasoline.
Amount of gasoline needed for 429 miles = 13 gallon.
Cost of gasoline for 1 gallon = $2.29
Cost of gasoline for 13 gallon = 13 × $2.29 = $29.77
Hence it will cost $29.77 for her to drive 429 miles.
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Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x - 68 = 34 - 8x. Your friend arrives at the incorrect answer x = -2. Find the correct value of x. Then find the error your friend possibly made. X x=0 What possible error could your friend have made to get x = -2? OA. Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side. OB. Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side. OC. Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x.
This is probably what steps your friend took, or something similar.
5x+4x-68 = 34-8x
9x = 34-8x-68
9x = -8x-34
9x+8x = -34
17x = -34
x = -34/17
x = -2
However, the error is when they subtracted 68 from both sides (line 2).
Instead, they should have added 68 to each side to undo the -68 on the left hand side.
----------------------------
Here's what the steps should look like (one variation of it anyway)
5x+4x-68 = 34-8x
9x = 34-8x+68
9x = -8x+102
9x+8x = 102
17x = 102
x = 102/17
x = 6 is the correct value of x
--------------------------
Check:
5x+4x-68 = 34-8x
5*6+4*6-68 = 34-8*6
30+24-68 = 34-48
54-68 = 34-48
-14 = -14
We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.
If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.
The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July
Answer:
the answer is 16 feet
Step-by-step explanation:
the population in Smalltown was 3,187 in 2017 . 148 more people moved to smalltown. in 2018 . 219 more people moved to smalltown . what was the population of smalltown in 2018 ?
Answer:
3080983
Step-by-step explanation:
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The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.
OA. True
OB. False
Answer:
B. False
Step-by-step explanation:
You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.
Cone lateral areaEffectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...
A = πrs
For the given dimensions (s=2h), the lateral area is ...
A = πr(2h) = 2πrh
Cylinder lateral areaThe lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...
A = 2πrh
ComparisonThe lateral areas of the given figures are both 2πrh, so one is not half the other.
The proposition is False.
For each of the right triangles, determine the measure of the missing side. Leave the measures in
exact form if irrational.
(if u can please show the work so i can get a better understanding)
Using the Pythagorean theorem, the missing sides are:
1. 5
2. 13
3. √15
4. 3
How to Apply the Pythagorean Theorem?The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.
1. Missing side = √(3² + 4²) [Pythagorean theorem]
Missing side = 5
2. Missing side = √(12² + 5²) [Pythagorean theorem]
Missing side = 13
3. Missing side = √(4² - 1²) [Pythagorean theorem]
Missing side = √15
4. Missing side = √((√10)² - 1²) [Pythagorean theorem]
Missing side = √(10 - 1) = √9
Missing side = 3
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what does the 9 represent in the number 53.89
What is the graetest comon factor on 18 12
Answer: 6
Step-by-step explanation:
Answer:
GCF = 2
Step-by-step explanation:
A patient in therapy jogged 7 km, 2 km, and 4 km. How many miles did that patient jog?
Answer:
7 + 2 + 4 = 13 km
13 km x 0.62 = 8.06
The answer is about 8.06 miles
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Translate this phrase into an algebraic expression.
67 decreased by twice a number
Use the variable n to represent the unknown number.
Answer:
2n-67
Step-by-step explanation:
Twice a number means 'multiply by 2' so we can write 2 x n. We can also write this in a simpler form- 2n
'67 decreased' means minus 67 off your answer so therefore the answer must be:
2n-67
Love answering your questions by the way :)
Which is the order from least to greatest of the following: seventh fifths, 0.4, one-eighth, seventy-five percent?
A. 0.4, seventy-five percent, seven-fifths, one eighth
B. one-eighth, 0.4, seventy-five percent, seven fifths
C. 0.4, one-eighth, seventy-five percent, seven fifths
D. seventy five percent, one-eighth, 0.4, seven fifths
BTW this is FLVS
The order from least to greatest of the numbers will be B. one eighth, 0.4, seventy five percent, seven fifths.
How to oder the numbers?It should be noted that 7/5 = 1.4
It should be noted that 1/8 = 0.125
It should be noted that 75% = 0.75
Therefore, the ordering of the numbers from least to greatest will be one eighth, 0.4, seventy five percent, seven fifths.
In conclusion, the correct option is B.
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Answer:
b
Step-by-step explanation:
(2,−3) and (0,−8) answer
Answer:
y2-y1/x2-x1
-8--3/0-2
Step-by-step explanation:
-8+3/-2=-5/-2=5/2
I need help with my homework
The lengths of the other two sides is 6 inches each.
The perimeter of any figure is sum of all the sides of the figure.
Here, we are given that the area of a triangle is 18 inches. Also, in the figure, we can see that the 3 sides of the triangle are-
6 inches, s inches and s inches.
Therefore, the perimeter of the given triangle will be-
Perimeter = 6 + s + s
⇒ 18 = 6 + s + s
Thus, the equation to find the lengths of the two sides is-
18 = 6 + 2s
18 - 6 = 2s
12 = 2s
2s = 12
s = 12/ 2
s = 6
Thus, the lengths of the other two sides is 6 inches.
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What is:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11
Answer:
-44
Step-by-step explanation:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11=-44
Hope this helps!
Answer:
-44
Step-by-step explanation:
Jan is saving money to buy a bike. The bike costs $255. She has $120 saved and each week she adds $15 to her savings. Write and solve an equation to find how long will it take her to save enough money to buy the bike.
Nina can swim 4 laps in 2 1/3 minutes. At this rate, how many laps can she swim in one minute
lap(s) in one minute
nina can swim 8/7 laps in one minute
given that
nina can swim 4 laps in 7/2 minutes
we have to calculate that how many laps can nina swim in 1 minute
then 4 laps= 7/2 minutes
then 4*2 /7 =1 minute
8/7=1 minute
thus nina can swim 8/7 laps in one minute
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QUESTION 8
Simplify 6a+ (-12b) - 9b+8a
O 2a + 3b
O 14a-21b
O2a-21b
O 14a + 3b
After simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.
What are expressions?An expression is a collection of numbers or variables that have been combined using the operations +, -, × or ÷. Arithmetic expressions consist only of numbers and mathematical operators, whereas algebraic expressions consist of variables, numbers, and mathematical operators.So, 6a + (-12b) - 9b + 8a:
6a + (-12b) - 9b + 8a6a + -12b -9b + 8a6a - 21b + 8a14a - 21bTherefore, after simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.
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The correct question is given below:
Simplify 6a+ (-12b) - 9b+8a
A. 2a + 3b
B. 14a-21b
C. 2a-21b
D. 14a + 3b